Simplify the following expression: $z = \dfrac{t^2 - 3t - 54}{t - 9} $
Explanation: First factor the polynomial in the numerator. $ t^2 - 3t - 54 = (t - 9)(t + 6) $ So we can rewrite the expression as: $z = \dfrac{(t - 9)(t + 6)}{t - 9} $ We can divide the numerator and denominator by $(t - 9)$ on condition that $t \neq 9$ Therefore $z = t + 6; t \neq 9$